On the effective stress law and its application to finite deformation problems in a poroelastic solid

Abstract Certain materials, such as rubber and gel, can undergo relatively large deformations without failure; and elastic finite deformation theories have been developed. Porous materials, such as soil, clay, and sediment, can also undergo relatively large deformations, and the concept of effective stress is commonly introduced to formulate the constitutive laws. In this research, it is demonstrated that for a porous solid, the effective stress is work-conjugate only to the Green strain tensor and not to the other strain measures under the assumption of an incompressible solid constituent. Based on this finding, the previously reported hyperelastic model, in which the effective stress and the Hencky strain has an elastic linear relation, is questioned. Several alternative hyperelastic models developed for solid materials are tested for their suitability for porous solids. Certain constitutive models, such as the Saint Venant–Kirchhoff model, exhibit an apparent strain-softening in the elastic range, which is believed to be not consistent with the observed behavior of most porous materials. Other models, such as the Ogden model, show the potential for modeling finite deformations of fluid-saturated poroelastic materials. One-dimensional finite consolidation problems are numerically solved and compared with the analytical solution based on the infinitesimal deformation theory.